MATLAB: Eigenvalues and eigenvector manual calculation

eigenvalues eigenvectors matrix

I have a matrix 2×2, for example A= [ 0.064911 3.276493; 3.276493 311.2073]. I would like to calculate the eigenvalues and eigenvectors. I have calculated the eigenvalues by manual and match it with matlab is match. the manual of eigenvalues :
eigenvalues were calculated by |A- λ * I|=0
so I received the eigenvalues (0.0304;311.2418). Now I am trying to calculated the eigenvectors that I found the way like this
B= eig(A) ; this is calculating the eigenvalues
(v,d)=eig(A)
I got v= (-0.9999 0.0105; 0.0105 0.9999) and d = ( 0.0304 0 ; 0 311.2418).
I would like to ask how to calculate manual of matrix v? Hope someone can help. Thank you.

Best Answer

By solving
(A-lambda1*I)*v1 = 0
and
(A-lambda2*I)*v2 = 0
You could use
v1 = null(A-lambda1*I)
and
v2 = null(A-lambda2*I)
to achieve this.
Best wishes
Torsten.
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